The background of the invention will now be described with reference to the accompanying drawings in which:
FIG. 1 is a schematic block diagram of a known color conversion process; and
FIG. 2 illustrates various methods utilised in deriving a predetermined set of output values.
Referring now to FIG. 1, there is shown a simplified form of a prior art color copying process. Hitherto, an image which is to be copied is placed on a scanner 1 and scanned at a high resolution, commonly 600 dots per inch (dpi). In the full color scanning process, known to those skilled in the art, the scanned values produced for each pixel of the image on scanner 1 includes separate values for the Red, Green and Blue (RGB) color components. Hence, the scanned pixels can be plotted in a three dimensional RGB color space, also known as an additive color space. The scanned pixels are normally printed out on a printer 2, which normally prints an image by utilising multiple color passes. The printer 2, normally works in a subtractive color space such as a Cyan, Magenta and Yellow (CYM) color space, or a Cyan, Yellow, Magenta and blacK (CYMK) color space. In order to transfer color values from RGB space to CYMK or CYM space, it is necessary to determine the corresponding Cyan, Yellow, Magenta and blacK components for each possible Red, Green and Blue value which a pixel of the scanned image can take. As each color component of the input signal can take a large number of values, with common systems utilising eight bit color component values, giving 256 possible levels for each color component, the number of overall combinations of values for input pixels is extremely large (in this example over 16 million values).
In order to determine the mapping for any particular RGB--CYMK transfer function, a series of known RGB values can be printed out by the output device or printer 2 and their colormetric CYMK values can be measured using a colorimeter.
As the number of possible color points is excessively large, one method of determining a transfer function is to measure the color component values of a predetermined number of points and to derive a table with each entry being a 7 tuple (RGBCYMK) comprising the RGB values and corresponding CYMK values obtained from measurements. Points not in the table can then be derived by means of interpolation. The normal interpolation technique used is linear interpolation and an example of such a system is given in U.S. Pat. No. 3,893,166 by Pugsley, entitled "Color Correcting Image Reproduction Methods and Apparatus".
The predetermined points can be chosen utilising a number of criteria. Firstly, it is desirable that the points cover the whole of the color space. Secondly, the system utilised for interpolation can require the predetermined points to be, for example, evenly spaced within one or other of the color spaces. Alternatively, it can be desirable to increase the number of points where the color transfer function is not well behaved, at the expense of decreasing the number of points where the transfer function is well behaved, thereby giving an overall increase in accuracy for the interpolation process.
Unfortunately, the physical color conversion process is known to be a highly non-linear process with the actual color produced by printer 2 being dependent on a large number of factors including the type of inks used, the type of paper used and the type of scanners used to scan the image from scanner 1. Consequentially, given an initial set of sample points, it is unclear how to derive a set of desired predetermined points from the set of sample points.
Referring now to FIG. 2, there will now be explained an example of two prior art color conversion processes. As stated previously, the color conversion process is a highly non-linear one and includes interactions between the various color components. Although the process is a multi-dimensional one, FIG. 2 shows a single slice through the multi-dimensional plane for constant green and blue for illustration of a particular transfer function between the Red component of an input image and the required Magenta output component.
It is assumed that, for a series of sample points, 30-38, the corresponding Red components 20-28 and corresponding Magenta components 40-48 are measured. This set of sample points can then be plotted on the Red-Magenta axes, and from this series of plots an overall curve or transfer function derived.
Unfortunately, once the sample points have been plotted, it is unclear as to what process should then be utilised to derive the corresponding magenta values of a set of predetermined points 12-19 on the red axis. A number of known methods can be used, however, each of these methods have a number of significant disadvantages. In a first method known as Lagrange interpolation, a polynomial 9 is fitted to the sample data such that it passes through each of the sample data points. Use of Lagrange interpolation often produces inadequate results for those sample points which are not well behaved (i.e. do not substantially conform to a linear relationship) and the Lagrange interpolation can result in a transfer function having excessive oscillation thereby producing unrealistic results.
A second known method is that known as "least squares" which, in its simplest form, fits a straight line, 10, in the vicinity of the given data points such that the sum of the squares of the distances of those points from the straight line is minimised, where the distance is measured in the vertical direction. Unfortunately, the least squares method can itself lead to a substantial reduction in the fidelity of the transfer function as -much detail is lost. The fitting of quadratics and higher order polynomials utilising a least squared methodology is also known to those skilled in the art but goes only part of the way to solving this problem of fidelity loss.
A third method of deriving the transfer function can consist of constructing straight line segments between the various data points. However, this method can lead to large discontinuities of derivatives at the various end points. In the color conversion process, such a transfer function has been found to produce unacceptable results with banding and other artifacts being found in certain images.